Preface xiii Chapter One. Choice, Preference, and Utility 1 1.1. Consumer Choice: The Basics 1 1.2. Proving Most of Proposition 1.2, and More 5 1.3. The No-Better-Than Sets and Utility Representations 7 1.4. Strict Preference and Indifference 9 1.5. Infinite Sets and Utility Representations 10 1.6. Choice from Infinite Sets 15 1.7. Equivalent Utility Representations 17 1.8. Commentary 18 Bibliographic Notes 23 Problems 23 Chapter Two. Structural Properties of Preferences and Utility Functions 30 2.1. Monotonicity 31 2.2. Convexity 32 2.3. Continuity 35 2.4. Indifference Curve Diagrams 38 2.5. Weak and Additive Separability 39 2.6. Quasi-linearity 43 2.7. Homotheticity 44 Bibliographic Notes 45 Problems 45 Chapter Three. Basics of Consumer Demand 50 3.1. The Consumer's Problem 50 3.2. Basic Facts about the CP 52 3.3. The Marshallian Demand Correspondence and Indirect Utility Function 54 3.4. Solving the CP with Calculus 56 Bibliographic Notes 63 Problems 64 Chapter Four. Revealed Preference and Afriat's Theorem 67 4.1. An Example and Basic Ideas 67 4.2. GARP and Afriat's Theorem 70 4.3. Comparative Statics and the Own-Price Effect 74 Bibliographic Notes 77 Problems 78 Chapter Five. Choice under Uncertainty 79 5.1. Two Models and Three Representations 79 5.2. The Mixture-Space Theorem 89 5.3. States of Nature and Subjective Expected Utility 101 5.4. Subjective and Objective Probability and the Harsanyi Doctrine 108 5.5. Empirical and Theoretical Critiques 110 Bibliographic Notes 116 Problems 116 Chapter Six. Utility for Money 123 6.1. Properties of Utility Functions for Money 123 6.2. Induced Preferences for Income 134 6.3. Demand for Insurance and Risky Assets 138 Bibliographic Notes 140 Problems 140 Chapter Seven. Dynamic Choice 148 7.1. The Standard Strategic Approach 149 7.2. Dynamic Programming 152 7.3. Testable Restrictions of the Standard Model 153 7.4. Three Alternatives to the Standard Model 156 Bibliographic Notes 161 Problems 161 Chapter Eight. Social Choice and Efficiency 166 8.1. Arrow's Theorem 166 8.2. What Do We Give Up? 172 8.3. Efficiency 175 8.4. Identifying the Pareto Frontier: Utility Imputations and Bergsonian Social Utility Functionals 176 8.5. Syndicate Theory and Efficient Risk Sharing: Applying Proposition 8.10 184 8.6. Efficiency? 192 Bibliographic Notes 194 Problems 194 Chapter Nine. Competitive and Profit-Maximizing Firms 197 9.1. The Production-Possibility Set 198 9.2. Profit Maximization 199 9.3. Basics of the Firm's Profit-Maximization Problem 201 9.4. Afriat's Theorem for Firms 207 9.5. From Profit Functions to Production-Possibility Sets 211 9.6. How Many Production-Possibility Sets Give the Same Profit Function? 213 9.7. What Is Going On Here, Mathematically? 216 9.8. Differentiability of the Profit Function 219 9.9. Cost Minimization and Input-Requirement Sets 222 9.10. Why DoWe Care? 228 Bibilographic Notes 229 Problems 229 Chapter Ten. The Expenditure-Minimization Problem 233 10.1. Defining the EMP 233 10.2. Basic Analysis of the EMP 235 10.3. Hicksian Demand and the Expenditure Function 236 10.4. Properties of the Expenditure Function 238 10.5. How Many Continuous Utility Functions Give the Same Expenditure Function? 240 10.6. Recovering Continuous Utility Functions from Expenditure Functions 247 10.7. Is an Alleged Expenditure Function Really an Expenditure Function? 248 10.8. Connecting the CP and the EMP 254 Bibliographic Notes 255 Problems 255 Chapter Eleven. Classic Demand Theory 258 11.1. Roy's Identity and the Slutsky Equation 258 11.2. Differentiability of Indirect Utility 262 11.3. Duality of Utility and Indirect Utility 269 11.4. Differentiability of Marshallian Demand 274 11.5. Integrability 279 11.6. Complements and Substitutes 283 11.7. Integrability and Revealed Preference 284 Bibliographic Notes 286 Problems 287 Chapter Twelve. Producer and Consumer Surplus 289 12.1. Producer Surplus 289 12.2. Consumer Surplus 296 Bibliographic Notes 304 Problems 304 Chapter Thirteen. Aggregating Firms and Consumers 306 13.1. Aggregating Firms 307 13.2. Aggregating Consumers 310 13.3. Convexification through Aggregation 318 Bibliographic Notes 326 Problems 326 Chapter Fourteen. General Equilibrium 329 14.1. Definitions 329 14.2. Basic Properties ofWalrasian Equilibrium 333 14.3. The Edgeworth Box 335 14.4. Existence ofWalrasian Equilibria 338 14.5. The Set of Equilibria for a Fixed Economy 351 14.6. The Equilibrium Correspondence 354 Bibliographic Notes 354 Problems 355 Chapter Fifteen. General Equilibrium, Efficiency, and the Core 358 15.1. The First Theorem ofWelfare Economics 359 15.2. The Second Theorem ofWelfare Economics 362 15.3. Walrasian Equilibria Are in the Core 366 15.4. In a Large Enough Economy, Every Core Allocation Is a Walrasian-Equilibrium Allocation 370 15.5. Externalities and Lindahl Equilibrium 380 Bibliographic Notes 383 Problems 383 Chapter Sixteen. General Equilibrium, Time, and Uncertainty 386 16.1. A Framework for Time and Uncertainty 386 16.2. General Equilibrium with Time and Uncertainty 389 16.3. Equilibria of Plans, Prices, and Price Expectations: I. Pure Exchange with Contingent Claims 392 16.4. EPPPE: II. Complex Financial Securities and Complete Markets 402 16.5. EPPPE: III. Complex Securities with Real Dividends and Complete Markets 418 16.6. Incomplete Markets 419 16.7. Firms 424 Bibliographic Notes 431 Problems 432 About the Appendices 437 Appendix One: Mathematical Induction 439 Appendix Two: Some Simple Real Analysis 441 A2.1. The Setting 441 A2.2. Distance, Neighborhoods, and Open and Closed Sets 441 A2.3. Sequences and Limits 445 A2.4. Boundedness, (Completeness), and Compactness 446 A2.5. Continuous Functions 447 A2.6. Simply Connected Sets and the Intermediate-Value Theorem 448 A2.7. Suprema and Infima; Maxes and Mins 448 A2.8. The Maximum of a Continuous Function on a Compact Set 449 A2.9. Lims Sup and Inf 450 A2.10. Upper and Lower Semi-continuous Functions 451 Appendix Three: Convexity 452 A3.1. Convex Sets 452 A3.2. The Separating- and Supporting-Hyperplane Theorems 457 A3.3. The Support-Function Theorem 459 A3.4. Concave and Convex Functions 461 A3.5. Quasi-concavity and Quasi-convexity 463 A3.6. Supergradients and Subgradients 466 A3.7. Concave and Convex Functions and Calculus 468 Appendix Four: Correspondences 469 A4.1. Functions and Correspondences 470 A4.2. Continuity of Correspondences 471 A4.3. Singleton-Valued Correspondences and Continuity 474 A4.4. Parametric Constrained Optimization Problems and Berge's Theorem 475 A4.5. Why this Terminology? 477 Appendix Five: Constrained Optimization 479 Appendix Six: Dynamic Programming 485 A6.1. Several Examples 485 A6.2. A General Formulation 489 A6.3. Bellman's Equation 494 A6.4. Conserving and Unimprovable Strategies 496 A6.5. Additive Rewards 501 A6.6. States of the System 504 A6.7. Solving Finite-Horizon Problems 506 A6.8. Infinite-Horizon Problems and Stationarity 509 A6.9. Solving Infinite-Horizon (Stationary) Problems with Unimprovability 512 A6.10. Policy Iteration (and Transience) 516 A6.11. Value Iteration 518 A6.12. Examples 521 A6.13. Things Not Covered Here: Other Optimality Criteria; Continuous Time and Control Theory 527 A6.14. Multi-armed Bandits and Complexity 528 A6.15. Four More Problems You Can Solve 530 Appendix Seven: The Implicit Function Theorem 534 Appendix Eight: Fixed-Point Theory 535 References 543 Index 551
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